Estimation of a covariance matrix with location: Asymptotic formulas and optimal B-robust estimators

Werner A. Stahel

Journal of Multivariate Analysis, 1987, vol. 22, issue 2, 296-312

Abstract: Applying the non-singular affine transformations AZ + [mu] to a spherically symmetrically distributed variate Z generates the covariance-location model, indexed by the parameters AAT and [mu], consisting of so-called elliptical distributions. We develop an algebraic machinery that simplifies the derivation of influence functions and asymptotic variance-covariance matrices for equivariant estimators of [Sigma] and [mu] and reveals a natural structure of [Sigma]. In addition, optimal B-robust estimators are derived.

Keywords: covariance; matrix; multivariate; location; elliptical; distributions; equivariant; estimation; robust; estimation; optimal; B-robust; estimation; asymptotic; formulas (search for similar items in EconPapers)
Date: 1987
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